Threshold Dynamics of a Semiconductor Single Atom Maser

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

Figure 1

(a) Optical micrograph of the DQD SeSAM. The source-drain bias $V_{\mathrm{SD}}$ is applied through an $LC$ filtered bias tee. The cavity is connected to input and output ports with coupling rates ${\kappa }_{\mathrm{in}}$ and ${\kappa }_{\mathrm{out}}$. Inset: SEM image of an InAs nanowire DQD. (b) $I_e$ as a function of $V_L$ and $V_R$ with $V_{\mathrm{SD}}=2\mathrm{mV}$. (c) $I_e$ (black) and $P_{\mathrm{out}}$ (red) plotted as a function of $\epsilon$.

Figure 2

(a) Upper panel: Pulse sequence used to tune the time-averaged current flowing through the device. A square wave with a period $\tau =50\mathrm{ns}$ and duty cycle $D$ is applied to toggle the current on and off. The resulting time-averaged current is ${\overline{I}}_e=D{I}_{\mathrm{on}}$. Lower panel: DQD level configuration with the current on (left panel) and off (right panel). (b) The measured ${\overline{I}}_e$ (red circles) as a function of $D$. The solid line is the prediction ${\overline{I}}_e=D{I}_{\mathrm{on}}$.

Figure 3

(a) Time series $Q(t)$ with ${\overline{I}}_e$ ranging from 1.7 nA to 3.8 nA with a step size of 0.3 nA. The data are offset along the $x$ axis by 250 in $Q$ for clarity. The emission amplitude increases with increasing ${\overline{I}}_e$. (b)–(d) $IQ$ histograms acquired with ${\overline{I}}_e=1.7$, 2.9, and 4 nA. (b) The emission is centered around $(I,Q)=(0,0)$ at small currents. (c) The distribution gradually broadens as ${\overline{I}}_e$ is increased. (d) With ${\overline{I}}_e=4\mathrm{nA}$, the histogram has a ring shape indicative of above-threshold maser emission.

Figure 4

$P_{\mathrm{out}}$ (red circles) as a function of ${\overline{I}}_e$ and fits to theory (solid lines) for two different devices. (a) Device 1 crosses threshold around ${\overline{I}}_e\approx 2.6\mathrm{nA}$. (b) Device 2 crosses threshold around ${\overline{I}}_e\approx 6.1\mathrm{nA}$. Both devices exhibit qualitatively similar threshold behavior.